In the present article, we extended the idea of the linguistic intuitionistic fuzzy set to linguistic interval-valued intuitionistic fuzzy (LIVIF) set to represent the data by the interval-valued linguistic terms of membership and non-membership degrees. Some of the desirable properties of the proposed set are studied. Also, we propose a new ranking method named as possibility degree measures to compare the two or more different LIVIF numbers. During the aggregation process, some LIVIF weighted and ordered weighted aggregation operators are proposed to aggregate the collections of the LIVIF numbers. Finally, based on these proposed operators and possibility degree measure, a new group decision making approach is presented to rank the different alternatives. A real-life case has been studied to manifest the practicability and feasibility of the proposed group decision making method.

H. Garg and K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Computing, 22(2018), 4959-4970.
doi: 10.1007/s00500-018-3202-1.Google Scholar

H. Garg and K. Kumar,
Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis, Arabian Journal for Science and Engineering, 43 (2018), 3213-3227.
doi: 10.1007/s13369-017-2986-0.Google Scholar

H. Garg and K. Kumar, An advanced study on the similarity measures of intuitionistic fuzzy sets based on the set pair analysis theory and their application in decision making, Soft Computing, 22(2018), 4959-4970.
doi: 10.1007/s00500-018-3202-1.Google Scholar

H. Garg and K. Kumar,
Some aggregation operators for linguistic intuitionistic fuzzy set and its application to group decision-making process using the set pair analysis, Arabian Journal for Science and Engineering, 43 (2018), 3213-3227.
doi: 10.1007/s13369-017-2986-0.Google Scholar